Question

the relationship between womens whole-number shoe sizes and foot lengths is an arithmetic sequence, where \\(a_n\\) is the foot length in inches that corresponds to a shoe size of \\(n\\). a womens size 7 fits a foot \\(9\frac{1}{3}\\) inches long, and a womens size 12 fits a foot 11 inches long. what is the explicit formula for the arithmetic sequence? round to the nearest hundredth, if necessary.

\\(a_n = -17.91 + 2.99(n - 1)\\)
\\(a_n = -5 + 2.99(n - 1)\\)
\\(a_n = 7 + 0.33(n - 1)\\)
\\(a_n = 7.35 + 0.33(n - 1)\\)

Explanation:

Identify the given terms

Using the Arithmetic Sequences knowledge point

$$
LATEXBLOCK0
$$

Find the common difference

Using the Arithmetic Sequence Explicit Formula knowledge point

$$
LATEXBLOCK1
$$

Find the first term

Using the Arithmetic Sequence Explicit Formula knowledge point

$$
LATEXBLOCK2
$$

Write the explicit formula

Using the Arithmetic Sequence Explicit Formula knowledge point

$$ a_n = 7.35 + 0.33(n - 1) $$

Answer:

• (A) \(a_n = -17.91 + 2.99(n-1)\)
• (B) \(a_n = -5 + 2.99(n-1)\)
• (C) \(a_n = 7 + 0.33(n-1)\)
• (D) \(a_n = 7.35 + 0.33(n-1)\) (Correct answer)